Question

How to find the slope of a line containing (8,5) (-4,7)?

Answer 1

Given any two points on a straight line, `(x_1,y_1)` and `(x_2,y_2)`
the slope is defined as
`(Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1)`

For the given points `(8,5)` and `(-4,7)`
we have
slope `= (7-5)/((-4)-8) = 2/(-12) = -1/6`

Answer 2

• `color(green)(Slope= (Rise)/(Run)`

The `Rise` is the Difference of the Y coordinates of any two points on the line
And the `Run` is the Difference of the X coordinates of those two points

• If the coordinates of the points are `(x_1,y_1) and (x_2,y_2)`, then #Slope = (y_2-y_1)/(x_2-x_1)#
  Here, the coordinates are `(8,5)` and `(-4,7)`

`Slope = (7-5)/(-4-8)=2/-12=-1/6`

The slope of the line passing through points `(8,5)` and `(-4,7)` is `color(green)(-1/6`

• The graph of the line will look like this:

graph{y=(-x/6)+(38/6) [-16.01, 16.02, -8, 8.03]}